Directed Graphs and Network Flows · Medium problem

A flow network has arcs $s\to a$ (capacity $6$), $a\to b$ (capacity $3$), $b\to t$ (capacity $5$), and $a\to t$ (capacity $4$), all carrying no flow yet. First push the path $s\to a\to b\to t$ to its bottleneck. Then push the path $s\to a\to t$ to ITS bottleneck (using the remaining residual capacity of $s\to a$). What is the total flow value after both pushes?